This application relates to optical dispersion in optical materials, and more specifically, to techniques and systems for using tunable Bragg gratings for dispersion management and compensation.
Many optical fibers and other optical transmission media may exhibit various dispersion effects including the chromatic dispersion and the polarization mode dispersion (PMD). An optical pulse can be broadened or distorted after propagation through a distance in such a dispersive optical medium. These dispersion effects can be undesirable and even adverse for certain applications such as optical communication systems where information is encoded, processed, and transmitted in optical pulses. The pulse broadening caused by the dispersion can limit the transmission bit rate, the transmission bandwidth, and other performance factors of the optical communication systems.
Dispersion devices may be used to add artificially-controlled dispersion to the dispersion in the optical signal caused by the transmission medium to modify or control the total dispersion in an optical signal. In dispersion compensation applications, for example, a dispersion device may be designed to produce dispersion that substantially cancels the dispersion caused by the transmission medium. At a given location in an optical link, however, the dispersion in an optical signal may change over time due to factors such as fluctuations in the dispersion caused by variations in temperature or stress in a given optical path of the signal and changes in the physical path of the signal due to switching or routing operations of the nodes. Therefore, it may be desirable to dynamically tune such dispersion compensation or control in response to those and other changes in the dispersion.
One tunable dispersion device is a nonlinearly-chirped fiber Bragg grating (FBG). See, U.S. Pat. No. 5,982,963 to Feng et al. The nonlinearly-chirped Bragg grating is a grating formed along an optical waveguide, e.g., an optical fiber. The grating has a grating parameter neff(z)xcex9(z) that changes nonlinearly with the position z along the fiber optic axis, where neff(z) is the effective index of refraction and xcex9(z) is the period of the grating. In operation, this nonlinearly-chirped grating reflects light satisfying a Bragg condition of xcex(z)=2neff(z)xcex9(z) and transmits light that fails to satisfy the Bragg condition. Hence, different spectral components are reflected back at different positions in the grating to produce different group delays. A Bragg reflection band centered at a center wavelength xcex0 can be generated and the bandwidth, xcex94xcexFBG, of the grating is determined by the chirping range of the grating parameter neff(z)xcex9(z).
Notably, due to the nonlinearity in the chirp of the grating parameter neff(z)xcex9(z), the relative group delays for different spectral components vary nonlinearly as a function of wavelength in the nonlinearly-chirped fiber grating. The grating dispersion D at a particular wavelength, which is the slope of the curve representing the group delay as a function of wavelength, may be tuned by adjusting the grating parameter neff(z)xcex9(z). For example, the grating period xcex9(z) may be changed to tune the grating dispersion D by stretching or compressing the fiber grating.
The nonlinear group delay T in the wavelength domain produced by the grating in a reflected optical signal at xcex may be generally expressed in the following polynomial expansion:
T=D0(2)(xcex0)(xcexxe2x88x92xcex0)+D0(3)(xcex0)(xcexxe2x88x92xcex0)2/2+D0(4)(xcex0)(xcexxe2x88x92xcex0)3/6+xe2x80x83xe2x80x83(1) 
where xcex0 is the center wavelength of the Bragg reflection band of the grating, D0(2)(xcex0) is a coefficient representing the second-order dispersion for which the group delay varies as a linear function of wavelength, D0(3)(xcex0) is a coefficient representing the third-order dispersion for which the group delay varies as a quadratic function of wavelength, and D0(4)(xcex0) is a coefficient representing the fourth-order dispersion for which the group delay varies as a cubic function of wavelength, and so on. The dispersion effects of the third order and higher orders are caused by the nonlinearity of the group delay generated by the spatial grating pattern. For simplicity, only the first two nonlinear terms are shown. The induced dispersion, D, produced by this grating can be represented by                                                         D              =                                                ⅆ                  T                                                  ⅆ                  λ                                                                                                        =                                                                    D                    0                                          (                      2                      )                                                        ⁢                                      (                                          λ                      0                                        )                                                  +                                                                            D                      0                                              (                        3                        )                                                              ⁡                                          (                                              λ                        0                                            )                                                        ⁢                                      xe2x80x83                                    ⁢                                      (                                          λ                      -                                              λ                        0                                                              )                                                  +                                                      D                    0                                          (                      4                      )                                                        ⁢                                      xe2x80x83                                    ⁢                                                                                    (                                                  λ                          -                                                      λ                            0                                                                          )                                            2                                        /                    2                                                  +                …                                                                        (        2        )            
Hence, the 2nd, 3rd, and 4th order dispersion terms lead to constant, linear, and quadratic variation in the dispersion with respect to the frequency detuning from the center of the Bragg reflection band, respectively. The corresponding rate of change in the induced dispersion in Eq. (2), i.e., the dispersion slope, of this nonlinearly-chirped fiber grating can be written as                     Slope        =                                            ⅆ              D                                      ⅆ              λ                                =                                                    D                0                                  (                  3                  )                                            ⁡                              (                                  λ                  0                                )                                      ⁢                          xe2x80x83                        +                                          D                0                                  (                  4                  )                                            ⁢                              xe2x80x83                            ⁢                              (                                  λ                  -                                      λ                    0                                                  )                                      +            …                                              (        3        )            
Hence, the grating dispersion D in the nonlinearly-chirped FBG is a function of the frequency detuning, i.e., the relative spectral position of the wavelength xcex of the input optical signal with respect to the center wavelength xcex0 of the Bragg reflection band.
Therefore, spectral components in an optical signal at different input wavelengths are located at different spectral positions with respect to the center wavelength and hence experience different grating dispersions upon being reflected by the grating. In addition, the grating dispersion D at each given input wavelength may be tuned by changing the grating parameter neff(z)xcex9(z) to shift the center wavelength xcex0 of the Bragg reflection band and hence the dispersion curve with respect to the input wavelength. For example, the total length of the fiber grating may be changed by using a fiber stretcher to adjust xcex9(z) in order to shift the center wavelength xcex0. This capability in tuning the grating dispersion can be used to control or compensate for dispersion in an optical signal after transmitting through an optical link with a time-varying dispersion.
The present disclosure includes techniques and fiber systems that use two fiber Bragg gratings as a pair to produce a tunable grating dispersion in an input optical signal. Each fiber Bragg grating is designed to have a spatial grating pattern that produces a nonlinear group delay with respect to the frequency detuning of the input optical signal from the center wavelength of a Bragg reflection band. At least one of the two gratings is tunable. In one embodiment, such a pair of tunable fiber Bragg gratings may be arranged in various configurations to produce a tunable grating dispersion based on nonlinear dispersion effects from the two gratings without exhibiting a net nonlinear dispersion effect. The spatial grating patterns of the two fiber Bragg gratings, such as nonlinear spatial chirps in nonlinearly-chirped gratings, may also be configured so that the grating dispersion and grating dispersion slope may be separately adjusted in a nearly independent manner.